What is the directrix y^2+8y+4x+20=0 ?

The directrix y^2+8y+4x+20=0 is x=0

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directrix y^2+8y+4x+20=0

directrix

y^{2} + 8 y + 4 x + 20 = 0

x = 0

Solution steps

Rewrite

y^{2} + 8 y + 4 x + 20 = 0

in the standard form

4 (- 1) (x - (- 1)) = (y - (- 4))^{2}

(h, k) = (- 1, - 4), p = - 1

Parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis, a distance

- p

from the center

(- 1, - 4)

x-coordinate

x = - 1 - p

x = - 1 - (- 1)

Refine

x = 0

- x^{2} + 4

y = + 2 (x + 1)^{2} - 5

x - x^{2}

x^{2} + 2 x - 16 y + 65 = 0

2 x^{2} - 36 x + 324